# Simple vs Compound Interest

Interest is payment for the use of money for a specified period of time, Interest can be calculated on either a simple or a compound basis. The distinction between the two is important because it affects the amount of interest earned or incurred.

## Simple Interest

Simple interest means that the interest payment is computed on only the amount of the principal for one or more periods. That is, if the original principal of the note is not changed, the interest payment will remain the same for each period.

## Formula to Calculate Simple Interest

*Where,*

- I = Simple Interest in dollars
- P = Principal amount
- i = Interest rate
- n = Number of periods

### Example

For example, if you invested $10,000 at 12% interest for 3 years, your yearly interest income would be $1,200 ($10,000 x .12). The total interest earned over the 3 years would be $3,600, and you would eventually receive $13,600 ($10,000 + $3,600).

I = Pin

I = $10,000 x 0.12 x 3

I = $3,600

## Compound Interest

Compound interest means that interest is computed on the principal of the note plus any interest that has accrued to date. That is, when compound interest is applied, the accrued interest of that period is added to the amount on which future interest is to be computed. Thus, by compounding, interest is earned or incurred not only on the principal but also on the interest left on deposit.

### Example

To demonstrate the concept of compound interest, assume that the interest in the previous example now will be compounded annually rather than on a simple basis. As the following table shows, in this case, your total interest income will be $4,049.28 rather than the $3,600 in the simple interest case.

During year 1, interest income is $1,200, or 12% of $10,000. Because the interest is compounded, it is added to the principal to determine the accumulated amount of $11,200 at the end of the year. Interest in year 2 is thus $1,344.00, or 12% of $11,200, and the accumulated amount at the end of year 2 is now $12,544.00. The interest and the accumulated amount at the end of year 3 are calculated in the same manner.

### Formulas to Calculate Compound Amount and Compound Interest

The following formulas are used to compute the Compound Amount and Compound Interest:

### Compound Amount Formula

*Where,*

- A = Compound Amount
- P = Principal Interest
- i = rate of interest
- n = number of periods

### Compound Interest Formula

Compound Interest = Compound Amount – Principal Amount

#### Example

The TD Bank has issued a loan of $2,000 to a sole proprietor for a period of 5-year at an interest rate of 7%. The interest is compounded annually.

**Required: **Compute (1). Compound Amount, (2). Compound Interest

#### Solution:

**Computation of Compound Amount:**

A = P (1 + i)^{n }

A = $2,000 (1 + 7%)^{5 }

A = $2,000 (1 + 0.07)^{5 }

A = $2,000(1.07)^{5 }

A = $2,000 (1.40)

A = $2,800

**Computation of Compound Interest:**

Compound interest = Compound Amount – Principal Amount

= $2,800 – $2,000

= $800

### Interest Compounded More Often Than Annually

Interest can be compounded as often as the lender desires. The more often interest is compounded, the more quickly it will increase. For example, many savings and loans institutions compound interest daily. This means that interest is calculated on the beginning balance of your account on each day. This interest is then added to the accumulated amount to determine the base for the next day’s interest calculation. Clearly this is more advantageous than if interest is compounded yearly.

When calculating interest that is compounded more than annually, it is quite easy to make the necessary adjustments. If interest is compounded more than annually, there is more than one interest period each year. For example? if interest is compounded quarterly, there are four interest periods in each year. In our example of a 3-year investment, there would be 12 interest period if interest were compounded quarterly.

But the interest rate that is stated in annual terms must be reduced accordingly. Thus, instead of using an interest rate of 12% in our example, the interest rate would be 3% each quarter. As a general rule, the annual interest rate is divided by the number of compounding periods to determine the proper interest rate each period.

if interest is compounded quarterly in the previous $10,000, 12% example, It will equal $4,257.60, and the total amount of the investment will grow to $14,257.60. This is shown in the following table:

Thus, in this straightforward example, the total interest increases by $208.32, from $4,049.28 to $4,257.60, when interest is compounded quarterly instead of annually.